We report a measurement of the top-quark mass using events collected by the CDF II detector from pp collisions at s√=1.96 TeV at the Fermilab Tevatron. We calculate a likelihood function for the top-quark mass in events that are consistent with tt→bℓ−νℓbℓ'+ν′ℓ decays. The likelihood is formed as the convolution of the leading-order matrix element and detector resolution functions. The joint likelihood is the product of likelihoods for each of 33 events collected in 340 pb−1 of integrated luminosity, yielding a top-quark mass Mt=165.2±6.1(stat)±3.4(syst) GeV/c2. This first application of a matrix-element technique to tt→bℓ+νℓbℓ'−ν¯ℓ′ decays gives the most precise single measurement of Mt in dilepton events. Combined with other CDF run II measurements using dilepton events, we measure Mt=167.9±5.2(stat)±3.7(syst) GeV/c2.